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Results tagged with homotopy-theory
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user 4262
Homotopy theory is an important sub-field of algebraic topology. It is mainly concerned with the properties and structures of spaces which are invariant under homotopy. Chief among these are the homotopy groups of spaces, specifically those of spheres. Homotopy theory includes a broad set of ideas and techniques, such as cohomology theories, spectra and stable homotopy theory, model categories, spectral sequences, and classifying spaces.
1
vote
Controlling Reflective Subcategories and Localizations
This may not be the sort of thing you're looking for (and it only answers your first question), but...
A category C is always both reflective and coreflective in the category $C^{\mathbf{2}}$ of arro …
- 3,622
5
votes
Accepted
An explicit description of Lawvere's segment in the category of simplicial sets
I've never heard this called 'Lawvere's segment' before, but your $L$ is the subobject classifier in the presheaf topos $[A^{\mathrm{op}},\mathrm{Set}]$. In presheaf toposes generally, the subobject …
- 3,622